Problem: Solve for $x$ and $y$ using elimination. ${-6x+2y = -10}$ ${5x+2y = 23}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${6x-2y = 10}$ $5x+2y = 23$ Add the top and bottom equations together. $11x = 33$ $\dfrac{11x}{{11}} = \dfrac{33}{{11}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-6x+2y = -10}\thinspace$ to find $y$ ${-6}{(3)}{ + 2y = -10}$ $-18+2y = -10$ $-18{+18} + 2y = -10{+18}$ $2y = 8$ $\dfrac{2y}{{2}} = \dfrac{8}{{2}}$ ${y = 4}$ You can also plug ${x = 3}$ into $\thinspace {5x+2y = 23}\thinspace$ and get the same answer for $y$ : ${5}{(3)}{ + 2y = 23}$ ${y = 4}$